{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright (c) 2015-2017 [Sebastian Raschka](sebastianraschka.com)\n",
    "\n",
    "https://github.com/rasbt/python-machine-learning-book\n",
    "\n",
    "[MIT License](https://github.com/rasbt/python-machine-learning-book/blob/master/LICENSE.txt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python Machine Learning - Code Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 11 - Working with Unlabeled Data – Clustering Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka \n",
      "last updated: 2017-01-03 \n",
      "\n",
      "CPython 3.5.2\n",
      "IPython 5.1.0\n",
      "\n",
      "numpy 1.11.3\n",
      "pandas 0.19.1\n",
      "matplotlib 1.5.3\n",
      "scipy 0.18.1\n",
      "sklearn 0.18.1\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,pandas,matplotlib,scipy,sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "*The use of `watermark` is optional. You can install this IPython extension via \"`pip install watermark`\". For more information, please see: https://github.com/rasbt/watermark.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Grouping objects by similarity using k-means](#Grouping-objects-by-similarity-using-k-means)\n",
    "  - [K-means++](#K-means++)\n",
    "  - [Hard versus soft clustering](#Hard-versus-soft-clustering)\n",
    "  - [Using the elbow method to find the optimal number of clusters](#Using-the-elbow-method-to-find-the-optimal-number-of-clusters)\n",
    "  - [Quantifying the quality of clustering via silhouette plots](#Quantifying-the-quality-of-clustering-via-silhouette-plots)\n",
    "- [Organizing clusters as a hierarchical tree](#Organizing-clusters-as-a-hierarchical-tree)\n",
    "  - [Performing hierarchical clustering on a distance matrix](#Performing-hierarchical-clustering-on-a-distance-matrix)\n",
    "  - [Attaching dendrograms to a heat map](#Attaching-dendrograms-to-a-heat-map)\n",
    "  - [Applying agglomerative clustering via scikit-learn](#Applying-agglomerative-clustering-via-scikit-learn)\n",
    "- [Locating regions of high density via DBSCAN](#Locating-regions-of-high-density-via-DBSCAN)\n",
    "- [Summary](#Summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import Image\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Grouping objects by similarity using k-means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "X, y = make_blobs(n_samples=150, \n",
    "                  n_features=2, \n",
    "                  centers=3, \n",
    "                  cluster_std=0.5, \n",
    "                  shuffle=True, \n",
    "                  random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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c5DBxchmjO5UXa1MvhDf2rTJLqZhRaV6KmVUzvpViZnVNpcrJvxu89D6zEuMm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\nmZmZmZXkwsnMzMyspH8BD4pTk/RRkNwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dc36e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c='white', marker='o', s=50)\n",
    "plt.grid()\n",
    "plt.tight_layout()\n",
    "#plt.savefig('./figures/spheres.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v0rdvX6pVq4abmxu1a9dm8ODBZGUZ9jnUqlWLPn365Gl/44038Pf312mbO3cuDRs2pGTJ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\nRERERKQTEyciIiIinf4/op2eGoKT7AsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddc6160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "km = KMeans(n_clusters=3, \n",
    "            init='random', \n",
    "            n_init=10, \n",
    "            max_iter=300,\n",
    "            tol=1e-04,\n",
    "            random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "\n",
    "plt.scatter(X[y_km == 0, 0],\n",
    "            X[y_km == 0, 1],\n",
    "            s=50,\n",
    "            c='lightgreen',\n",
    "            marker='s',\n",
    "            label='cluster 1')\n",
    "plt.scatter(X[y_km == 1, 0],\n",
    "            X[y_km == 1, 1],\n",
    "            s=50,\n",
    "            c='orange',\n",
    "            marker='o',\n",
    "            label='cluster 2')\n",
    "plt.scatter(X[y_km == 2, 0],\n",
    "            X[y_km == 2, 1],\n",
    "            s=50,\n",
    "            c='lightblue',\n",
    "            marker='v',\n",
    "            label='cluster 3')\n",
    "plt.scatter(km.cluster_centers_[:, 0],\n",
    "            km.cluster_centers_[:, 1],\n",
    "            s=250,\n",
    "            marker='*',\n",
    "            c='red',\n",
    "            label='centroids')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.tight_layout()\n",
    "#plt.savefig('./figures/centroids.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-means++"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hard versus soft clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the elbow method to find the optimal number of clusters "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distortion: 72.48\n"
     ]
    }
   ],
   "source": [
    "print('Distortion: %.2f' % km.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XXoFnn826EjMzs/KUeXDKlz4H7zhgMPCEpDHAKODjx9hGxPvA08D49NCuJFOO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f00ebe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distortions = []\n",
    "for i in range(1, 11):\n",
    "    km = KMeans(n_clusters=i, \n",
    "                init='k-means++', \n",
    "                n_init=10, \n",
    "                max_iter=300, \n",
    "                random_state=0)\n",
    "    km.fit(X)\n",
    "    distortions.append(km.inertia_)\n",
    "plt.plot(range(1, 11), distortions, marker='o')\n",
    "plt.xlabel('Number of clusters')\n",
    "plt.ylabel('Distortion')\n",
    "plt.tight_layout()\n",
    "#plt.savefig('./figures/elbow.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantifying the quality of clustering  via silhouette plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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p/SCldF1K6dKU0odTSv/d8rp7D9VtxZMj4qcR8aeIuCgi9mrb1hsj4qqI+EtE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\nm1Vb2ItlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f1f3c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import cm\n",
    "from sklearn.metrics import silhouette_samples\n",
    "\n",
    "km = KMeans(n_clusters=3, \n",
    "            init='k-means++', \n",
    "            n_init=10, \n",
    "            max_iter=300,\n",
    "            tol=1e-04,\n",
    "            random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "\n",
    "cluster_labels = np.unique(y_km)\n",
    "n_clusters = cluster_labels.shape[0]\n",
    "silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n",
    "y_ax_lower, y_ax_upper = 0, 0\n",
    "yticks = []\n",
    "for i, c in enumerate(cluster_labels):\n",
    "    c_silhouette_vals = silhouette_vals[y_km == c]\n",
    "    c_silhouette_vals.sort()\n",
    "    y_ax_upper += len(c_silhouette_vals)\n",
    "    color = cm.jet(float(i) / n_clusters)\n",
    "    plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n",
    "             edgecolor='none', color=color)\n",
    "\n",
    "    yticks.append((y_ax_lower + y_ax_upper) / 2.)\n",
    "    y_ax_lower += len(c_silhouette_vals)\n",
    "    \n",
    "silhouette_avg = np.mean(silhouette_vals)\n",
    "plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
    "\n",
    "plt.yticks(yticks, cluster_labels + 1)\n",
    "plt.ylabel('Cluster')\n",
    "plt.xlabel('Silhouette coefficient')\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/silhouette.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparison to \"bad\" clustering:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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z56lQoQJdu3Z1KPaoMDVr1mT/ge949913Wfb+e6zcY3TM6tapxbR/jGHcuHFU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\nZBALJyIiIiKDWDgRERERGfT/AY9THtt7edQkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f1f35f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "km = KMeans(n_clusters=2,\n",
    "            init='k-means++',\n",
    "            n_init=10,\n",
    "            max_iter=300,\n",
    "            tol=1e-04,\n",
    "            random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "\n",
    "plt.scatter(X[y_km == 0, 0],\n",
    "            X[y_km == 0, 1],\n",
    "            s=50,\n",
    "            c='lightgreen',\n",
    "            marker='s',\n",
    "            label='cluster 1')\n",
    "plt.scatter(X[y_km == 1, 0],\n",
    "            X[y_km == 1, 1],\n",
    "            s=50,\n",
    "            c='orange',\n",
    "            marker='o',\n",
    "            label='cluster 2')\n",
    "\n",
    "plt.scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1],\n",
    "            s=250, marker='*', c='red', label='centroids')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.tight_layout()\n",
    "#plt.savefig('./figures/centroids_bad.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XowqltLrqEtpix0mSJCmTwUmSJCmTwUmSJM2Luu+mA4OTJGkeTLCQMY5lgoVVlyK1xcnh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\nSVImg5MkSVImg5MkSVKm/w9PBCSXjbd8QQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11000df60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cluster_labels = np.unique(y_km)\n",
    "n_clusters = cluster_labels.shape[0]\n",
    "silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n",
    "y_ax_lower, y_ax_upper = 0, 0\n",
    "yticks = []\n",
    "for i, c in enumerate(cluster_labels):\n",
    "    c_silhouette_vals = silhouette_vals[y_km == c]\n",
    "    c_silhouette_vals.sort()\n",
    "    y_ax_upper += len(c_silhouette_vals)\n",
    "    color = cm.jet(float(i) / n_clusters)\n",
    "    plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n",
    "             edgecolor='none', color=color)\n",
    "\n",
    "    yticks.append((y_ax_lower + y_ax_upper) / 2.)\n",
    "    y_ax_lower += len(c_silhouette_vals)\n",
    "    \n",
    "silhouette_avg = np.mean(silhouette_vals)\n",
    "plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
    "\n",
    "plt.yticks(yticks, cluster_labels + 1)\n",
    "plt.ylabel('Cluster')\n",
    "plt.xlabel('Silhouette coefficient')\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/silhouette_bad.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Organizing clusters as a hierarchical tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Cg5VEMfGU3Kc7mTVCVWW0c/suhVsxHT6ssD4lkXom96MB/Wz+ODKYjcS6oZj2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QGSlvt8Wl2pnmlZWueAOtx1j39gC5fXNoHX3lYf2jy3Acw0TcHGCBl3nyAzW25eZa8HIHnXc3Pt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\nXl9F0uspB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Ng0FyGnI2FS4Y5sSH/yyAHJFDKGrNEhpbjxAxRR3FFZNz18kT1xUNYCsMTj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h+UBzBvOErOIDZFlTf/vtt3swS9xBgwb50wo4tYBxwdjV+JVb7PSI9YsUiBSIFIgAthN5QEIG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\nZCxAAiRAAiRAAiRAAiSQSwL/A13kqhIGoT+6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 11,
     "metadata": {
      "image/png": {
       "width": 400
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./images/11_05.png', width=400) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>Z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ID_0</th>\n",
       "      <td>6.964692</td>\n",
       "      <td>2.861393</td>\n",
       "      <td>2.268515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_1</th>\n",
       "      <td>5.513148</td>\n",
       "      <td>7.194690</td>\n",
       "      <td>4.231065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_2</th>\n",
       "      <td>9.807642</td>\n",
       "      <td>6.848297</td>\n",
       "      <td>4.809319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_3</th>\n",
       "      <td>3.921175</td>\n",
       "      <td>3.431780</td>\n",
       "      <td>7.290497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_4</th>\n",
       "      <td>4.385722</td>\n",
       "      <td>0.596779</td>\n",
       "      <td>3.980443</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             X         Y         Z\n",
       "ID_0  6.964692  2.861393  2.268515\n",
       "ID_1  5.513148  7.194690  4.231065\n",
       "ID_2  9.807642  6.848297  4.809319\n",
       "ID_3  3.921175  3.431780  7.290497\n",
       "ID_4  4.385722  0.596779  3.980443"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(123)\n",
    "\n",
    "variables = ['X', 'Y', 'Z']\n",
    "labels = ['ID_0', 'ID_1', 'ID_2', 'ID_3', 'ID_4']\n",
    "\n",
    "X = np.random.random_sample([5, 3])*10\n",
    "df = pd.DataFrame(X, columns=variables, index=labels)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performing hierarchical clustering on a distance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID_0</th>\n",
       "      <th>ID_1</th>\n",
       "      <th>ID_2</th>\n",
       "      <th>ID_3</th>\n",
       "      <th>ID_4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ID_0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.973534</td>\n",
       "      <td>5.516653</td>\n",
       "      <td>5.899885</td>\n",
       "      <td>3.835396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_1</th>\n",
       "      <td>4.973534</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.347073</td>\n",
       "      <td>5.104311</td>\n",
       "      <td>6.698233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_2</th>\n",
       "      <td>5.516653</td>\n",
       "      <td>4.347073</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.244262</td>\n",
       "      <td>8.316594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_3</th>\n",
       "      <td>5.899885</td>\n",
       "      <td>5.104311</td>\n",
       "      <td>7.244262</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.382864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_4</th>\n",
       "      <td>3.835396</td>\n",
       "      <td>6.698233</td>\n",
       "      <td>8.316594</td>\n",
       "      <td>4.382864</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          ID_0      ID_1      ID_2      ID_3      ID_4\n",
       "ID_0  0.000000  4.973534  5.516653  5.899885  3.835396\n",
       "ID_1  4.973534  0.000000  4.347073  5.104311  6.698233\n",
       "ID_2  5.516653  4.347073  0.000000  7.244262  8.316594\n",
       "ID_3  5.899885  5.104311  7.244262  0.000000  4.382864\n",
       "ID_4  3.835396  6.698233  8.316594  4.382864  0.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.spatial.distance import pdist, squareform\n",
    "\n",
    "row_dist = pd.DataFrame(squareform(pdist(df, metric='euclidean')),\n",
    "                        columns=labels,\n",
    "                        index=labels)\n",
    "row_dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can either pass a condensed distance matrix (upper triangular) from the `pdist` function, or we can pass the \"original\" data array and define the `metric='euclidean'` argument in `linkage`. However, we should not pass the squareform distance matrix, which would yield different distance values although the overall clustering could be the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>row label 1</th>\n",
       "      <th>row label 2</th>\n",
       "      <th>distance</th>\n",
       "      <th>no. of items in clust.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cluster 1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.521973</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.729603</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 3</th>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>8.539247</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 4</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>12.444824</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           row label 1  row label 2   distance  no. of items in clust.\n",
       "cluster 1          0.0          4.0   6.521973                     2.0\n",
       "cluster 2          1.0          2.0   6.729603                     2.0\n",
       "cluster 3          3.0          5.0   8.539247                     3.0\n",
       "cluster 4          6.0          7.0  12.444824                     5.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1. incorrect approach: Squareform distance matrix\n",
    "\n",
    "from scipy.cluster.hierarchy import linkage\n",
    "\n",
    "row_clusters = linkage(row_dist, method='complete', metric='euclidean')\n",
    "pd.DataFrame(row_clusters,\n",
    "             columns=['row label 1', 'row label 2',\n",
    "                      'distance', 'no. of items in clust.'],\n",
    "             index=['cluster %d' % (i + 1)\n",
    "                    for i in range(row_clusters.shape[0])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>row label 1</th>\n",
       "      <th>row label 2</th>\n",
       "      <th>distance</th>\n",
       "      <th>no. of items in clust.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cluster 1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.835396</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.347073</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 3</th>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.899885</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 4</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.316594</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           row label 1  row label 2  distance  no. of items in clust.\n",
       "cluster 1          0.0          4.0  3.835396                     2.0\n",
       "cluster 2          1.0          2.0  4.347073                     2.0\n",
       "cluster 3          3.0          5.0  5.899885                     3.0\n",
       "cluster 4          6.0          7.0  8.316594                     5.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. correct approach: Condensed distance matrix\n",
    "\n",
    "row_clusters = linkage(pdist(df, metric='euclidean'), method='complete')\n",
    "pd.DataFrame(row_clusters,\n",
    "             columns=['row label 1', 'row label 2',\n",
    "                      'distance', 'no. of items in clust.'],\n",
    "             index=['cluster %d' % (i + 1) \n",
    "                    for i in range(row_clusters.shape[0])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>row label 1</th>\n",
       "      <th>row label 2</th>\n",
       "      <th>distance</th>\n",
       "      <th>no. of items in clust.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cluster 1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.835396</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.347073</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 3</th>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.899885</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 4</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.316594</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           row label 1  row label 2  distance  no. of items in clust.\n",
       "cluster 1          0.0          4.0  3.835396                     2.0\n",
       "cluster 2          1.0          2.0  4.347073                     2.0\n",
       "cluster 3          3.0          5.0  5.899885                     3.0\n",
       "cluster 4          6.0          7.0  8.316594                     5.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3. correct approach: Input sample matrix\n",
    "\n",
    "row_clusters = linkage(df.values, method='complete', metric='euclidean')\n",
    "pd.DataFrame(row_clusters,\n",
    "             columns=['row label 1', 'row label 2',\n",
    "                      'distance', 'no. of items in clust.'],\n",
    "             index=['cluster %d' % (i + 1)\n",
    "                    for i in range(row_clusters.shape[0])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S5JuBf8rMBwM3As8E/gT4Mj2sLxYRtwfWA0cCv2h6HkmSpNWiSRCbBD5cb98M7JKZvwJe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\nSZIKMYhJkiQV8v8BD7yUBDKesJ0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11077dc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.cluster.hierarchy import dendrogram\n",
    "\n",
    "# make dendrogram black (part 1/2)\n",
    "# from scipy.cluster.hierarchy import set_link_color_palette\n",
    "# set_link_color_palette(['black'])\n",
    "\n",
    "row_dendr = dendrogram(row_clusters, \n",
    "                       labels=labels,\n",
    "                       # make dendrogram black (part 2/2)\n",
    "                       # color_threshold=np.inf\n",
    "                       )\n",
    "plt.tight_layout()\n",
    "plt.ylabel('Euclidean distance')\n",
    "#plt.savefig('./figures/dendrogram.png', dpi=300, \n",
    "#            bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Attaching dendrograms to a heat map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sTLGxsZoyZYqKi4vl9/sDXrOhoUEPPfSQ+vXrp8jISN1xxx365JNPrPoVAMARmmaEgr2R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\nxjouQuYrsAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11077d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot row dendrogram\n",
    "fig = plt.figure(figsize=(8, 8), facecolor='white')\n",
    "axd = fig.add_axes([0.09, 0.1, 0.2, 0.6])\n",
    "\n",
    "# note: for matplotlib < v1.5.1, please use orientation='right'\n",
    "row_dendr = dendrogram(row_clusters, orientation='left')\n",
    "\n",
    "# reorder data with respect to clustering\n",
    "df_rowclust = df.iloc[row_dendr['leaves'][::-1]]\n",
    "\n",
    "axd.set_xticks([])\n",
    "axd.set_yticks([])\n",
    "\n",
    "# remove axes spines from dendrogram\n",
    "for i in axd.spines.values():\n",
    "        i.set_visible(False)\n",
    "\n",
    "# plot heatmap\n",
    "axm = fig.add_axes([0.23, 0.1, 0.6, 0.6])  # x-pos, y-pos, width, height\n",
    "cax = axm.matshow(df_rowclust, interpolation='nearest', cmap='hot_r')\n",
    "fig.colorbar(cax)\n",
    "axm.set_xticklabels([''] + list(df_rowclust.columns))\n",
    "axm.set_yticklabels([''] + list(df_rowclust.index))\n",
    "\n",
    "# plt.savefig('./figures/heatmap.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applying agglomerative clustering via scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster labels: [0 1 1 0 0]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "ac = AgglomerativeClustering(n_clusters=2, \n",
    "                             affinity='euclidean', \n",
    "                             linkage='complete')\n",
    "labels = ac.fit_predict(X)\n",
    "print('Cluster labels: %s' % labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Locating regions of high density via DBSCAN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ncW2Q/hYBn0nHrY9TOl/V6Z14ZmXuRWNPtmpOVjrvVBfy947h/C0CgtOq5gCC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\nHQUJp3MOgjIvDAFDoB4QoIxCUP75z3/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Mg12nRiC1Nkj9TeSeSPip7Lbddlsfv/CyEZGL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\n8cUXe+v3EUcc4U477TRfnvgmCvJfNKQLAUZoOfbZZx+/krMEBHM8ioN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BlPGVXFNuuVZD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\nQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 20,
     "metadata": {
      "image/png": {
       "width": 500
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./images/11_11.png', width=500) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WNnpe+BSPnlTJkPiqpDRMKUvnT78FXVApaFLQFEjhFUcy++FZ+hLu6OjKBkfe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\nmkREREQCUNAkIiIiEsD/DzM1VYYUuee1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110469dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=200, noise=0.05, random_state=0)\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/moons.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K-means and hierarchical clustering:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tBtdyMiWZ9UvfZfXsafTp04frr7/evk/79u3Ztm0b06ZN48NVKzh79iz169Vn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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11047b6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 3))\n",
    "\n",
    "km = KMeans(n_clusters=2, random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "ax1.scatter(X[y_km == 0, 0], X[y_km == 0, 1],\n",
    "            c='lightblue', marker='o', s=40, label='cluster 1')\n",
    "ax1.scatter(X[y_km == 1, 0], X[y_km == 1, 1],\n",
    "            c='red', marker='s', s=40, label='cluster 2')\n",
    "ax1.set_title('K-means clustering')\n",
    "\n",
    "ac = AgglomerativeClustering(n_clusters=2,\n",
    "                             affinity='euclidean',\n",
    "                             linkage='complete')\n",
    "y_ac = ac.fit_predict(X)\n",
    "ax2.scatter(X[y_ac == 0, 0], X[y_ac == 0, 1], c='lightblue',\n",
    "            marker='o', s=40, label='cluster 1')\n",
    "ax2.scatter(X[y_ac == 1, 0], X[y_ac == 1, 1], c='red',\n",
    "            marker='s', s=40, label='cluster 2')\n",
    "ax2.set_title('Agglomerative clustering')\n",
    "\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "#plt.savefig('./figures/kmeans_and_ac.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Density-based clustering:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7tuPpbbu30969e22+xk6dOnHTTTexZv4sdq5PNo63uLCQneuTWb8okQERo/AP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\nGQyaJEmSMhg0SZIkZfj/hsMYhadW6SQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1103014e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import DBSCAN\n",
    "\n",
    "db = DBSCAN(eps=0.2, min_samples=5, metric='euclidean')\n",
    "y_db = db.fit_predict(X)\n",
    "plt.scatter(X[y_db == 0, 0], X[y_db == 0, 1],\n",
    "            c='lightblue', marker='o', s=40,\n",
    "            label='cluster 1')\n",
    "plt.scatter(X[y_db == 1, 0], X[y_db == 1, 1],\n",
    "            c='red', marker='s', s=40,\n",
    "            label='cluster 2')\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "#plt.savefig('./figures/moons_dbscan.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "..."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
